Imaging techniques have been developed for studying organs where motion is present. For example, four-dimensional respiratory-correlated computed tomography (4D RCCT) has been widely used for studying organs where motion is associated with patient breathing. The current standard practice for reconstructing images with respect to such organ motion is to use phase binned images. However, the phase binning algorithm assumes that the patient has a periodic breathing pattern. When the patient's breathing is irregular as represented in the graph of FIG. 1A, this assumption breaks down and significant image artifacts like that indicated by the arrow of FIG. 1B are introduced.
A recent extensive study found that 90% of 4D RCCT patient images had at least one artifact. Amplitude binning algorithms have been developed as a way to alleviate these artifacts by assuming that the underlying anatomical configuration is correlated to the amplitude of the breathing signal.
For example, during a typical 4D RCCT fan-beam scan, the patient passes through the scanner on an automated couch that pauses at regular intervals to collect data. At each couch position slices are acquired repeatedly (e.g., 15-20 times). Each slice is acquired by collecting a series of projections at different angles. The slices are then reconstructed individually using filtered back-projection. The speed of acquisition of each slice is dependent on the scanner and for current generation multi-slice scanners is generally on the order of 0.5 s. The X-ray detection process used to acquire slices is subject to Poisson noise. However, at the X-ray tube currents typically used in clinical practice the signal is strong enough that the noise is approximately Gaussian. The patient's breathing is monitored during acquisition using an external surrogate for internal organ motion. The resulting breathing trace, a(t), is used to tag the acquired projection retrospectively with a breathing amplitude. An example of a breathing trace monitoring system is the Real-time Position Management (RPM) system (Varian Oncology Systems, Palo Alto, Calif.), which uses a camera to track infrared-reflective markers attached to the patient's torso.
Although application of amplitude binning algorithms in the foregoing example may reduce binning artifacts, since data is not acquired at all breathing amplitudes the images often have some missing slices. Accordingly, image artifacts continue to be present in the reconstructed images.
Modeled rigid 2D motion has been used during image acquisition to alleviate in-plane artifacts in fan-beam CT. However, such rigid 2D motion models are not valid for imaging of the torso, where respiratory-induced motion causes highly non-linear deformation with a significant component in the superior-inferior direction.
Another prior method reconstructs a full 4D time-indexed image using a B-spline motion model and a temporal smoothing condition. Yet other B-spline-based methods require an artifact-free reference image (such as a breath-hold image) in addition to a 4D fan-beam or cone-beam scan. These approaches address difficulties caused by slowly-rotating cone-beam scanners. However, the acquisition of an artifact-free reference image remains impractical for many radiotherapy patients. While the B-spline model guarantees smooth deformations, it cannot guarantee the diffeomorphic properties for large deformations and it does not directly enforce local conservation of tissue volume.
In another previous method, 3D images are reconstructed at arbitrary amplitudes by interpolating each slice from those collected at nearby amplitudes and then stacking them. Two slices are used to interpolate a slice at the desired amplitude using an optical flow algorithm, so only 2D motion can be estimated. A more recent approach has used a 4D cone-beam scan to estimate organ motion using an optical flow approach. The motion estimate is then used to correct for organ motion during subsequent 3D scans on the fly. This method may be useful in reducing artifacts in a 3D image, but the optical flow model, like the B-spline model, does not ensure diffeomorphic incompressible motion estimates.
As early as 1991, an incompressible optical flow method for image registration was used. Some systems have used a spline-based model which penalizes tissue compression to perform incompressible image registration. Other researches have studied incompressible fluid-based registration of liver computed tomography (CT). An incompressible fluid-based approach solves Poisson's equation via a multigrid method at each iteration. Another efficient Fourier method of incompressible projection applies a result from the continuous domain to discrete data without alteration, which does not accommodate the discrete nature of image data. Despite these efforts in image registration, the incompressible nature of internal organs has not previously been incorporated into the image reconstruction process.
Deformable image registration has been shown to be useful in tracking organ motion in artifact-free 4D RCCT images. Such methods may be used with either phase or amplitude binned images, but are challenged in the presence of binning artifacts. That is, deformable image registration is not well suited for use with respect to 4D RCCT images which include binning artifacts.
From the above, it can be appreciated that regeneration of images where motion is present is problematic. In particular, motion artifacts remain present despite application of many of the available image reconstruction techniques. Moreover, none of the present imaging reconstruction techniques guarantee the diffeomorphic properties for large deformations or directly enforce local conservation of object volume.